Tabletop Quantum Gravity: Probing Spacetime via Massive Superposition — E8 Intelligence Research

FINDING: Quantum gravity experiments are transitioning from theoretical speculation to tabletop-scale tests probing the quantum nature of spacetime via superposition of massive systems. MATH: The core experimental framework relies on the quantum superposition of a mass \\( m \\) in two spatial locations separated by \\( \\Delta x \\), generating a gravitational phase shift \\( \\Delta \\phi = \\frac{G m^2 \\Delta t}{\\hbar \\Delta x} \\) (for two masses in superposition, per Bose–Marletto–Vedral proposal). The decoherence timescale for gravitational entanglement is \\( \\tau \\sim \\frac{\\hbar \\Delta x}{G m^2} \\). Penrose's criterion for gravitationally-induced collapse: \\( E_G = \\frac{G m^2}{\\Delta x} \\) compared to \\( \\hbar/\\tau \\). CONNECTION: The ratio \\( \\frac{G m^2}{\\hbar c} \\) (gravitational coupling) is dimensionless and tiny (~\\(10^{-45}\\) for protons), but the experimental geometry uses harmonic oscillator frequencies and lattice-like trap spacings — the optimal \\( \\Delta x \\) often scale Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com